How Do the Pieces Move?

Rooks

Rooks move up/down (vertically) or left/right (horizontally). They can move 1 or more squares, but in only one continuous direction each time (they cannot move left and then up in the same move).

Bishops

Bishops move diagonally:

Bishops move along diagonals. They move 1 or more squares, but they can only move in one direction each time (e.g. they cannot zig-zag in the same move). Bishop moves along a diagonal need to stay on the same color square as they start from (if the Bishop has moved to a different color square, then it's a mistake and an illegal move). So you'll find that one of your bishops always moves along light squares, and the other bishop is always on dark squares.

Queens

Queens move like Rooks plus Bishops.

Queens can do any of the moves of either a Rook or a Bishop. So the Queen can move up/down or left/right like a Rook, or diagonally like a Bishop.

Knights

Knights are the only pieces that jump over other pieces. They move in a 2-1 or 1-2 pattern, it's an "L" shaped move. The Knights do not ever slide, so they cannot be blocked by pieces, they always jump over pieces between the two squares. This is a tricky move for beginners to get right.

Kings

Kings move slowly, only 1 square.

Kings can move to any of the 8 squares that are right next to it: up/down, left/right, and the diagonals. But the King can only move 1 square at a time. It's pretty slow-moving.

Pawns

Pawns are tricky little slow-movers.

The rules for Pawn moves are tricky: they can move forwards 1 or 2 squares only, but captures are diagonal only, and Pawns cannot go backwards.

Pawn forward moves:
Pawns can move straight forwards only 1 square at a time, except for each pawn's very first move, where it can move 2-squares (or 1 square if you wish).
But these straight moves cannot capture, they must move into an empty square.
These forwards moves must be vertically upwards, not diagonally.

Pawn 2-move starter move:
Pawns can move 2-squares forwards on their very first move.
They must move into an empty square.
But once a pawn has done it's 2-move starter move, it then can only move 1 square after that.
The 2-move starter move cannot jump over a piece either.
And these 2-square moves are only forwards, upwards, not diagonally.

Pawns only capture diagonally:
Pawn capture moves are the opposite of its normal non-capturing moves.
Capture moves are diagonal only, and the Pawn can only move diagonally when capturing.
This is the opposite of the normal Pawn moves, because pawn forward moves cannot capture and cannot be diagonal.
A pawn capture must be diagonal, and pawns can only move diagonally when capturing an enemy piece or pawn.
A pawn can only capture diagonally 1-square, it can never capture diagonally 2 or more squares (i.e. cannot do Bishop moves).

Pawns move forwards only:
Pawns can only move forwards, and can only capture forwards too.
Pawns cannot move backwards ever (unlike all the other pieces), so you have to carefully consider how far to move them.

Pawns turn into Queens:
But sometimes it's good to push your pawn as far as you can, because Pawns turn into Queens when they get to the last square on the other side of the board, which is great to do!